pseudovector
Sign in to saveAlso known as axial vector, pseudovector quantity, space-oriented vector
thumb|right|A loop of wire (black), carrying a electric current|current I, creates a [[magnetic field B (blue). If the position and current of the wire are reflected across the plane indicated by the dashed line, the magnetic field it generates would not be reflected: Instead, it would be reflected and reversed. The position and current at any point in the wire are "true" vectors, but the magnetic field B is a pseudovector.]]
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13 sectionsContents
- Physical examples
- Details
- Behavior under addition, subtraction, scalar multiplication
- Behavior under cross products and curls
- Examples
- The right-hand rule
- Formalization
- Geometric algebra
- Transformations in three dimensions
- Note on usage
- See also
- Notes
- References
thumb|right|A loop of wire (black), carrying a electric current|current I, creates a [[magnetic field B (blue). If the position and current of the wire are reflected across the plane indicated by the dashed line, the magnetic field it generates would not be reflected: Instead, it would be reflected and reversed. The position and current at any point in the wire are "true" vectors, but the magnetic field B is a pseudovector.]]
In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations or translations, but which does not transform like a vector under certain discontinuous rigid transformations such as reflections. For example, the angular velocity of a rotating object is a pseudovector because, when the object is reflected in a mirror, the reflected image rotates in such a way so that its angular velocity "vector" is not the mirror image of the angular velocity "vector" of the original object; for true vectors (also known as polar vectors), the reflection "vector" and the original "vector" must be mirror images.